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On a Novel Resonant Ermakov-NLS System: Painlevé Reduction

In: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Author

Listed:
  • Colin Rogers

    (The University of New South Wales, School of Mathematics and Statistics and Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems)

  • Wolfgang K. Schief

    (The University of New South Wales, School of Mathematics and Statistics and Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems)

Abstract

A novel resonant Ermakov-NLS system is introduced which admits symmetry reduction to a hybrid Ermakov-Painlevé II system. If the latter is Hamiltonian then combination with a characteristic Ermakov invariant provides an algorithmic integration procedure. The latter involves the isolation of positive solutions of a concomitant integrable Painlevé XXXIV equation. Explicit expressions for a multi-parameter class of wave packet representations for the original Ermakov-NLS system are obtained via the iterated application of a Bäcklund transformation admitted by the canonical Painlevé II equation.

Suggested Citation

  • Colin Rogers & Wolfgang K. Schief, 2018. "On a Novel Resonant Ermakov-NLS System: Painlevé Reduction," Springer Books, in: Josef Dick & Frances Y. Kuo & Henryk Woźniakowski (ed.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pages 1081-1098, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-72456-0_49
    DOI: 10.1007/978-3-319-72456-0_49
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